[LeetCode] [DP] 118. Pascal's Triangle

118. Pascal's Triangle

 

Given an integer numRows, return the first numRows of Pascal's triangle.

In Pascal's triangle, each number is the sum of the two numbers directly above it as shown:

 

Example 1:

Input: numRows = 5

Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

 

Example 2:

Input: numRows = 1

Output: [[1]]

 

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        
        if numRows == 1:
            return [[1]]
        
        if numRows == 2:
            return [[1], [1,1]]
        
        blank =[]
        for zeros in range(numRows):
            blank.append( [ 0 for i in range(zeros+1) ] )

        for i in range(numRows):
            blank[i][0] = 1
            blank[i][-1] = 1 

        for i in range(2, numRows):
            for k in range(1,i):
                blank[i][k] = blank[i-1][k-1] + blank[i-1][k] 

        return blank

@credit to sherlock321

def generate(self, numRows):
        res = [[1]]
        for i in range(1, numRows):
            res += [map(lambda x, y: x+y, res[-1] + [0], [0] + res[-1])]
        return res[:numRows]

explanation: Any row can be constructed using the offset sum of the previous row. Example:

    1 3 3 1 0 
 +  0 1 3 3 1
 =  1 4 6 4 1